The Reformulated F-Index of Vertex and Edge F-Join of Graphs

Abstract

The valency based topological indices (TIs) are defined by algebraic functions as the chemical graph theory tools in which the structural parameters are used as input and the output is related with the topology of chemical species. In theoretical chemistry, the TIs are mainly used to investigate/develop the QSAR and QSPR investigations of the molecular graphs. The Reformulated F-index or RFI is one such kind of TIs. The RFI for a molecular graph Y is defined as $RF\left(Y\right)={\sum }_{uv\in E\left(Y\right)}{\left(d_Y\left(u\right)+d_Y\left(v\right)-2\right)}^3$ , where $d_Y\left(u\right)$ is the degree of a vertex $u$ in $Y$ . In this paper, we study the RFI for vertex and edge version of F-join of given general graphs which are related to subdivision and total graph.